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lfunc_lfunctions • Show schema
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{'Lhash': '5852953891437062777345522678021', 'a10': [37.05108789261704, -21.391455568570933], 'a2': [0.0, -5.0770632665980715], 'a3': [-4.426492333780264, -2.721427129096892], 'a4': [-17.77657141303948, 0.0], 'a5': [4.2133521772921405, 7.29774004125094], 'a6': [-13.816857709861278, 22.47358162771375], 'a7': [-4.299092404609986, -18.01437771605294], 'a8': [0.0, 49.63627159441556], 'a9': [12.187668762030897, 24.09275264777805], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7171203303616602, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [4.426492333780264, 2.721427129096892]]], [7, [[1.0, 0], [4.299092404609986, 18.01437771605294]]]], 'bad_primes': [3, 7], 'central_character': '63.5', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '510901615910469958241494193066', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.0770632665980715], [-8.0, 0]], [[1.0, 0], [4.426492333780264, 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'10.31155320950662347530518608277268', '12.33042422949851013376145065962055', '13.12552303078679829123215441714929', '14.67046323373308465886204987887407', '15.58794760120339084016829823085529'], 'prelabel': '2-63-63.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9279834880936249, 'root_angle': -0.28609284510525607, 'root_number': '-0.22483922567732545 - 0.9743958757080311*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.286092845105', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.61716650501588499961671011419', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.57124986013622512183044222257', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.41790592480155081875288040943', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7171203303616602, 'bad_primes': [3, 7], 'central_character': '63.5', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/4/i/a/5/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-63-63.5-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-63-63.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9279834880936249, 'root_angle': -0.28609284510525607, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.61716650501588499961671011419', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5852953891437062777345522678021', 'Lhash_array': ['5852953891437062777345522678021'], 'factors': ['2-63-63.5-c3-0-21'], 'label': '2-63-63.5-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/4/i/a/5/2'}